Remarks on functors. (You decide which one is not serious.)
- Someone ought to write a review of Mazzola under the title “Bring in ‘da noise, bring in ‘da functors.”
- There suddenly appears to me an angle from which an adjunction stands to an inversion as true belief to knowledge.*
- From this angle, moreover, the adjunction unexpectedly (and of course incompletely) reactivates the approximate group-structure in the large – this time not as something in thought (a reason) but as something which thought is in (and functions as cause?), which (note) are not two cases but one (viz. the case of the Two, or the great and small in appearance), the other being the flawless but entirely finite so-called-duality (rather identity itself!) of element and operation, and perhaps finally of reasons and causes too, in the group, that figure of the One which is neither unit nor totality but, one might say, falls immediately into forms (plural). The relation between reversibility with respect to adjunction and with respect to the One requires reflection. (That last unintended, but let it stand).
- Conjecture: As the group recovers, at the level of its arrows, the symmetry of its elements, so does the adjunction recover, at the level of its arrows, the asymmetry of its objects.
*Further explanation to follow.